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Joint Math-AMO/QO Physics Pizza Seminar

"Simple Connectivity in Polar Spaces with Group-Theoretic Applications"

Dr. Reed Nessler
University of Virginia


A projective space serves to capture the incidence geometry of subspaces in a vector space. Likewise, a polar space is defined having in mind the geometry of subspaces that are singular with respect to some additional structure (in the simplest case, a symmetric bilinear form). However, the axioms give rise to exceptional spaces in low dimensions that do not come from linear algebra: in projective geometry, these are the non-Desarguesian planes, while the polar spaces include a family of so-called nonembeddable spaces of rank 3.

Projective and polar spaces (rather, their flag complexes) are exactly the spherical buildings of type An and Cn, respectively. A spherical building is a union of simplicial spheres, and thus some elements are opposite others, i.e. antipodal on the sphere. Understanding the geometry of chambers opposite a given chamber provides information about groups acting on these buildings.

Wednesday, September 2, 2015
628 BLOC, 12:30 Noon
Blocker Building

Institute for Quantum Science and Engineering
Texas A&M University

(Pizza, salad, and soda to be served at 12:00 noon)